Covering a point set by two disjoint rectangles

Abstract

Given a set S of n points in the plane, the disjoint two-rectangle covering problem is to find a pair of disjoint rectangles such that their union contains S and the area of the larger rectangle is minimized. In this paper we consider two variants of this optimization problem: (1) the rectangles are free to rotate but must remain parallel to each other, and (2) one rectangle is axis-parallel but the other rectangle is allowed to have an arbitrary orientation. For both of the problems, we present O(n(2) log n)-time algorithms using O(n) space.